Related papers: On the automorphism groups of models in $\mathbb C…

The first-order theory of the automorphism group of an infinite resplendent model in a finite language is undecidable.

We give elementary proofs of the following two theorems on automorphisms of a finite group G: (1) An automorphism of G is inner if and only if it extends to an automorphism of every finite group containing G. (2) There exists a finite…

By a map we mean a $2$-cell decomposition of a closed compact surface, i.e., an embedding of a graph such that every face is homeomorphic to an open disc. Automorphism of a map can be thought of as a permutation of the vertices which…

We define the notion of invariant derivation of a C*-algebra under a compact quantum group action and prove that in certain conditions, such derivations are generators of one parameter automorphism groups.

Let us consider a polynomial algebra in three variables equipped with an integer grading. We construct a system of group-generating automorphisms that preserve a given grading.

The aim of this paper is to survey some aspects of mapping class groups with focus on their finite dimensional representations arising in topological quantum field theory.

$C_\infty$ Algebras and their morphisms are a framework in which one can study algebras and their maps that are not commutaive-associative but are homotopic to being that. In statistics cumulants measure the independence of random…

We discuss the computation of automorphism groups and normal forms of cones and polyhedra in Normaliz, and indicate its implementation via nauty. The types of automorphisms include integral, rational, Euclidean and combinatorial, as well as…

The principal observation of the present paper is that an inner isotopy (i.e. a principal isotopy defined by an algebra endomorphism) is a very helpful instrument in constructing and studying interesting classes of nonassociative algebras.…

We formulate a notion of the quantum automorphism group of a $2$-graph. After some preliminary computations, we define quantum isomorphism between a pair of $2$-graphs. We produce a `non-trivial' example of a pair of $2$-graphs that are not…

These expository notes are dedicated to the study of the topology of configuration spaces of manifolds. We give detailed computations of many invariants, including the fundamental group of the configuration spaces of $\mathbb{R}^2$, the…

We conjecture that the automorphism group of a topological parallelism on real projective 3-space is compact. We prove that at least the identity component of this group is, indeed, compact.

We initiate a systematic study of the perfection of affine group schemes of finite type over fields of positive characteristic. The main result intrinsically characterises and classifies the perfections of reductive groups, and obtains a…

In this article we present an extensive survey on the developments in the theory of non-abelian finite groups with abelian automorphism groups, and pose some problems and further research directions.

We will show that every element of a finitely generated abelian group is automorphically equivalent what we will define to be a {\em representative element} in a {\em repeat-free subgroup}, and for finite abelian groups we can count the…

Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…

An adjoint Chevalley group of rank at least 2 over a rational algebra (or a similar ring), its elementary subgroup, and the corresponding Lie ring have the same automorphism group. These automorphisms are explicitly described.

Let $G$ be a finite $p$-group and let Aut$(G)$ denote the full automorphism group of $G$. In the recent past, there has been interest in finding necessary and sufficient conditions on $G$ such that certain subgroups of Aut$(G)$ are equal.…

This is a biased survey for the Johnson homomorphisms of the automorphism groups of free groups. We just exposit some well known facts and recent developments for the Johnson homomorphisms and its related topics.

We apply results proved in [Li19] to the linear order expansions of non-trivial free homogeneous structures and the universal n-linear order for $n\geq 2$, and prove the simplicity of their automorphism groups.